Spectral analysis of the generalized shift-splitting preconditioned saddle point problem

Zhi Ru Ren, Yang Cao*, Qiang Niu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


A shift-splitting preconditioner was recently proposed for saddle point problems, which is based on a generalized shift-splitting of the saddle point matrix. We provide a new analysis to prove that the corresponding shift-splitting iteration method is unconditional convergent. To further show the efficiency of the shift-splitting preconditioner, the eigenvalue distribution of the shift-splitting preconditioned saddle point matrix is investigated. We show that all eigenvalues having nonzero imaginary parts are located in an intersection of two circles and all real eigenvalues are located in a positive interval. Numerical examples are given to confirm our theoretical results.

Original languageEnglish
Pages (from-to)539-550
Number of pages12
JournalJournal of Computational and Applied Mathematics
Publication statusPublished - 1 Feb 2017


  • Convergence
  • Eigenvalue estimate
  • Saddle point problem
  • Shift-splitting preconditioner

Cite this